Volume 519, September 2010
|Number of page(s)||12|
|Published online||16 September 2010|
Unevenly-sampled signals: a general formalism for the Lomb-Scargle periodogram
Chip Computers Consulting srl, Viale Don L. Sturzo 82,
S. Liberale di Marcon, 30020 Venice, Italy e-mail: firstname.lastname@example.org,
2 ESO, Karl Schwarzschild strasse 2, 85748 Garching, Germany
3 INAF - Osservatorio Astronomico di Trieste, via Tiepolo 11, 34143 Trieste, Italy e-mail: email@example.com
4 ESO, Karl Schwarzschild strasse 2, 85748 Garching, Germany e-mail: firstname.lastname@example.org
Accepted: 12 May 2010
The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a component other than noise, when a peak in the periodogram exceeds it. In the case of signals sampled on a regular time grid, determination of such a threshold is relatively simple. When the sampling is uneven, however, things are more complicated. The most popular solution in this case is to use the Lomb-Scargle periodogram, but this method can be used only when the noise is the realization of a zero-mean, white (i.e. flat-spectrum) random process. In this paper, we present a general formalism based on matrix algebra, which permits analysis of the statistical properties of a periodogram independently of the characteristics of noise (e.g. colored and/or non-stationary), as well as the characteristics of sampling.
Key words: methods: data analysis / methods: statistical
© ESO, 2010
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